Jacksonville State University JSU Digital Commons Theses Theses, Dissertations & Graduate Projects Spring 5-7-2021 Streaming Down the Stern-Brocot Tree: Finding and Expressing Solutions to Pell's Equation in SL(2,Z) Marcus L. Shell Jacksonville State University,
[email protected] Follow this and additional works at: https://digitalcommons.jsu.edu/etds_theses Part of the Algebra Commons, and the Number Theory Commons Recommended Citation Shell, Marcus L., "Streaming Down the Stern-Brocot Tree: Finding and Expressing Solutions to Pell's Equation in SL(2,Z)" (2021). Theses. 13. https://digitalcommons.jsu.edu/etds_theses/13 This Thesis is brought to you for free and open access by the Theses, Dissertations & Graduate Projects at JSU Digital Commons. It has been accepted for inclusion in Theses by an authorized administrator of JSU Digital Commons. For more information, please contact
[email protected]. STREAMING DOWN THE STERN-BROCOT TREE: FINDING AND EXPRESSING SOLUTIONS TO PELL'S EQUATION IN SL2(Z) A Thesis Submitted to the Graduate Faculty of Jacksonville State University in Partial Fulfillment of the Requirements for the Degree of Master of Science with a Major in Mathematics By MARCUS LEE SHELL Jacksonville, Alabama May 7, 2021 ABSTRACT This paper explores and elaborates on a method of solving Pell's equation as introduced by Norman Wildberger. In the first chapters of the paper, foundational topics are introduced in expository style including an explanation of Pell's equation. An explanation of continued fractions and their ability to express quadratic irrationals is provided as well as a connection to the Stern-Brocot tree and a convenient means of representation for each in terms of 2×2 matrices with integer elements.